How to Implement the New Math Standards, Part I
Arlyne LeSchack

Instructionally, this translates into a goal with three components:

• Conceptual Understanding
• Procedural Fluency
• Problem Solving

Conceptual Understanding
This consists of those relationships constructed internally and connected to already existing ideas. It involves the understanding of mathematical ideas and procedures and includes the knowledge of the basic arithmetic facts. Students use conceptual understanding of mathematics when they identify and apply principles, know and apply facts and definitions and compare and contrast related concepts. Further, knowledge learned with understanding provides the foundation for remembering mathematical methods and for solving new problems.

Procedural Fluency
This is the skill to carry out procedures flexibly and accurately. It includes algorithms, the step by step routines needed to perform the four arithmetic operations. Procedural fluency applies to other areas of mathematics as well, like the ability to use a protractor for measuring the size of an angle or how to use a calculator. Calculators are encouraged because if used properly they can enhance a students understanding and computing skills. With understanding, a students is less likely to make common computational errors. In the past, this might have been called having "number sense."

Problem Solving
Problem solving is the ability to formulate, represent and solve mathematical problems. Problems generally fall into three types: one step problems, multi-step problems and process problems. Most problems that we encounter in the real world are multi-step or process problems. In order to solve them, we have to integrate both conceptual understanding and procedural fluency.

But just knowing a concept or a procedure is not useful. Students must be taught how to analyze a problem and how to choose the most useful strategy to solve the problem. This means exposing the students to a broad range of strategies. Sometimes selecting a strategy is the most difficult part of the solution, so mathematics instruction must include when to apply certain strategies as well as how to apply a strategy.

Click here to read the next installment, process and content strands of the new standards.

If you have comments or questions, please contact me at aleschack@aol.com.